Pricing for Basket CDS and LCDS

Tao Wang, Jin Liang, Xiaoli Yang

Department of Mathematics, Tongji University, Shanghai, China.

DOI: 10.4236/me.2012.32024                

Abstract

In this paper, under the reduced form framework and “Bottom Up” method, a model for pricing a basket Loan-only Credit Default Swap (LCDS), with the negative correlation between prepayment and default, is established. A general pricing formula for it is obtained, where one factor CIR (Cox-Ingersoll-Ross) and ICIR (Inversed CIR) models are used to describe the negative correlation between prepayment and default. In this situation, the positivity of prepayment and default intensity processes are guaranteed. Numerical computations are presented.

Keywords

Basket Loan-Only Credit Default Swap; Prepayment Risk; Bottom Up; Reduced Form; One Factor ICIR Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. H. S. Shek, S. Uematsu and W. Zhen, “Valuation of Loan CDS and LCDX,” Stanford University, Stanford, 2007. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1008201
[2]	P. Dobranszky and W. Schoutens, “Generic Levy One-Factor Models for the Joint Modeling of Prepayment and Default: Modeling LCDX,” Katholieke Universiteit Leuven, Leuven, 2008. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1008201.
[3]	P. Collin-Dufresne and J. P. Harding, “A Closed Form Formula for Valuing Mortgages,” The Journal of Real Estate Finance and Economics, Vol. 74, No 2, 1999, pp. 133-146. doi:10.1023/A:1007879422329
[4]	J. B. Kau, D. C. Keenan and A. A. Smurov, “Reduced-Form Mortgage Valuation,” University of Georgia, Georgia, 2004. http://www.terry.uga.edu/realestate/docs/reducedform082504.pdf
[5]	J. M. Ma and J. Liang, “Valuation of Basket Credit Default Swaps by Partial Differential Equation Method,” Applied Mathematics A Journal of Chinese Universities, Vol. 23, No. 4, 2008, pp. 427-436.
[6]	T. Wang and J. Liang, “The Limitation and Efficiency of Formula Solution for Basket Default Swap Based on Vasicek Model,” Systems Engineering, Vol. 27, No. 5, 2009, pp. 49-54.
[7]	J. Liang, J. M. Ma, T. Wang and Q. Ji, “Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model,” Asia-Pacific Financial Markets, Vol. 18, No. 1, 2011, pp. 33-54. doi:10.1007/s10690-010-9119-z
[8]	W. Zhen, “Valuation of Loan CDS under Intensity Based Model,” Stanford University, Stanford, 2007. http://www.defaultrisk.com/pp_crdrv144.htm
[9]	J. Liang and T. Wang, “Valuation of Loan-Only Credit Default Swap with Negatively Correlated Default and Prepayment Intensities,” International Journal of Computer Mathematics, in Press.
[10]	J. Liang and Y. J. Zhou, “Valuation of a Tranche Loan Credit Default Swap Index,” Technology and Investment, Vol. 2, No. 4, 2011, pp. 240-246. doi:10.4236/ti.2011.24025
[11]	Y. J. Zhou and J. Liang, “Valuation of a Basket Loan Credit Default Swap,” International Journal of Financial Research, Vol. 1, No. 1, 2010, pp. 21-29.
[12]	Y. Wu and J. Liang, “Valuation of Loan Credit Default Swaps Correlated Prepayment and Default Risks with Stochastic Recovery Rate,” International Journal of Financial Research, in Press.
[13]	J. Liang, T. Wang and X. Yang, “Single Name LCDS Pricing and Related CVA Calculation regarding Counterparty Default,” Tongji University, Shanghai, 2011.
[14]	X. S. Qian, L. S. Jiang, C. L. Xu and S. Wu, “Explicit Formulas for Pricing of Mortgage-Backed Securities in a Case of Prepayment Rate Negatively Correlated to Interest Rate,” unpublished, 2009.
[15]	T. R. Hurd and A. Kuznetsov, “Explicit Formulas for Laplace Transforms of Stochastic Integrals,” Mcmaster University, Hamilton, 2006. http://www.math.mcmaster.ca/tom/StochIntHurdKuzn.pdf